I don't know for sure at all. But I did notice I didn't have a pet battle on horde in north east Stormsong valley on my horde when it was up. So I made a point to go there and do some quests, and the next time it was up it was up for both factions.

I don't know if it was quests or just exploration, but maybe that will help the discussion/help figure it out.

In addition to having to "unlock" WQs on an 120 alt (IIRC, it's just a quick chat with an NPC to unlock them if you've already gone through the process on another toon), it's possible that Pet Battle tracking was turned off on one of your toons. Check that you have it on:

Open your World Map on the toon that cannot see the Pet Battle WQs.

Click on the magnifying glass on the map's upper right corner.

Make sure you're tracking all Pet Battle related content.

There have been a few cases where an addon was interfering with Pet Battle WQs showing up, so if the above doesn't work, you can try that as well.